You are almost there. You will find that a white pickling stain (i.e. ben moore) applied by brush and then wiped will give the proper whitewash you are looking for. You must then coat the area with a non-yellowing water based polyurethane. This will ensure that the floor will remain white, otherwise it will turn amber if an oil-modified poly is applied. I would recommend at least four coats, given the fact that the floor is soft pine, go with five.